[select] Release the forced popup mount and add keepMounted prop

[atomiks]

Closes #5184.

Problem

Select.Portal set forceMount on trigger focus and never released it: after the first interaction the whole portal subtree — positioner, popup, and every item — stayed in the DOM for the lifetime of the page. The mount can't simply be dropped on close, because closed-trigger typeahead and autofill matching read labels, values, and disabled state from mounted items.

Changes

• forceMount becomes a transient, focus-scoped mount instead of a permanent latch. Closed-trigger typeahead can only receive keystrokes while the trigger is focused, so the hidden items are kept mounted exactly then: armed on trigger focus (as before), released on trigger blur and after a close completes with focus elsewhere. Autofill mounts the items for a single microtask to match the value, then releases. No snapshot of item data is taken, so the React 18 index-guessing hazards of the earlier mirror approach don't apply.
• The close-complete release is deferred by one macrotask. With no exit animation it would otherwise run before focus returns to the trigger, unmounting and remounting the entire list on every close — a node-identity test guards against this.
• Added keepMounted to Select.Portal, the only popup-family portal missing it.
• The positioner clears selectedIndex and selectedItemTextRef on unmount. A stale index made SelectItemText re-adopt the ref on remount, misaligning alignItemWithTrigger after option replacement.
• The registered item values (not just their count) live on the root rather than the positioner, so the dynamic-items reconciliation survives an unmount and prunes the value on any change to the registered values — including replacing the collection with one of equal size, which the previous size-only check missed even while permanently mounted.
• Focus checks use shadow-safe containment rather than element identity, so focus resting inside a composite or shadow-backed trigger still counts as trigger focus — and such internal focus moves no longer commit field blur (touched state, validationMode="onBlur").

Behavior change

Removing the selected item from the list while the select is closed and unmounted reconciles the value the next time the items mount (any focus on the trigger remounts them), instead of immediately — there is no DOM to observe the removal against while unmounted.

The select-specific Motion handbook section is removed: Select now animates like every other popup, so the generic recipes (AnimatePresence unmounting, or keepMounted with actionsRef manual unmounting) apply.

Follow-ups

• Combobox/Autocomplete's analogous sticky forceMounted latch is released the same way in a separate change.

• Pre-existing and unchanged by this PR: useAnimationsFinished's close-complete scan can miss a JS-driven exit animation that registers a frame late (e.g. Motion animating off state.open without actionsRef), applying hidden mid-exit to a kept-mounted popup. The sticky mount on master has the same scan and timing. The documented actionsRef recipe is unaffected because it disables the automatic scan.

• I have followed (at least) the PR section of the contributing guide.

[pkg-pr-new]

• base-ui-tanstack-start

• vite-css-base-ui-example

  pnpm add https://pkg.pr.new/mui/base-ui/@base-ui/react@5343
  

  pnpm add https://pkg.pr.new/mui/base-ui/@base-ui/utils@5343
  

commit: 9378037

[code-infra-dashboard]

Bundle size

Bundle	Parsed size	Gzip size
@base-ui/react	🔺+491B(+0.11%)	🔺+155B(+0.11%)

Details of bundle changes

Performance

Total duration: 1,136.01 ms +105.65 ms^(+10.3%) | Renders: 78 ⁽⁺⁰⁾ | Paint: 1,783.86 ms +175.85 ms^(+10.9%)

Test	Duration	Renders
Scroll Area mount (300 instances)	73.90 ms 🔺+19.54 ms(+35.9%)	3 (+0)

14 tests within noise — details

Metric alarms

Test	Metric	Change
Scroll Area mount (300 instances)	bench:paint	🔺 +21.03 ms

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